where \(\alpha _{n}\) , \(\beta _{n}\)  and \(\gamma _{n}\)  are
functions of the parameters of the equation.
This system of homogeneous linear equations
can be written in matrix form.
Then, we see that the system has non-trivial solutions
only if the
determinant of a tridiagonal coefficient matrix vanishes; such
condition is called `characteristic
equation' and determine the possible values
of some `free' parameter of the equation.
The characteristic equation
is also written as the continued fraction [1]}, [2]}
\(\beta _{0}=\frac{\alpha _{0}\gamma _{1}}{\beta _{1}-}\ \frac{\alpha _{1}\gamma _{2}}{\beta _{2}-}\ \frac{\alpha _{2}\gamma _{3}}{\beta _{3}-}\cdots .\) 
